Globalization, Inequality and Welfare · 2016. 9. 7. · Globalization, Inequality and Welfare Pol Antr as Harvard University Alonso de Gortari Harvard University Oleg Itskhoki Princeton

A Motivating ExampleEconomic Model

Calibration and Counterfactuals

Globalization, Inequality and Welfare

Pol AntrasHarvard University

Alonso de GortariHarvard University

Oleg ItskhokiPrinceton University

Harvard - September 7, 2016

Antras, de Gortari and Itskhoki Globalization, Inequality and Welfare 1 / 35



Introduction

I Trade integration raises real income but often increases inequality

I Standard approach to demonstrating and quantifying the gains fromtrade largely ignores trade-induced inequality

I Kaldor-Hicks compensation principle

I Two basic shortcomings with this approach:

I How much compensation/redistribution actually takes place?

I Is this redistribution costless, as the Kaldor-Hicks approach assumes?

I These issues are relevant not just for trade, but also for any policywith redistributive effects




Introduction











Introduction











Introduction











This Paper

I We study welfare implications of trade liberalization in a model inwhich trade affects income distribution...

I ... and in which redistribution policies are constrained by informationfrictions (Mirrlees, 1971)

I We propose two types of adjustments to standard welfare measures:

1. A welfarist correction reflecting the preferences of aninequality-averse social planner (c.f., Atkinson, 1970)

2. A costly-redistribution correction capturing behavioral responses totrade-induced shifts across marginal tax rates




This Paper









This Paper









Building Blocks

I Skeleton of Trade Model: Itskhoki (2008)

I Melitz (2003) with heterogeneous worker/entrepeneurs and a laborsupply decision

I Welfarist correction: constant degree of inequality- (or risk-) aversion

I widely used in Public Finance and Macro (veil of ignorance rationale)

I Costly Redistribution: nonlinear progressive income tax system

I After-tax income is log-linear function of pre-tax income (Heathcoateet al., 2014)

I Model calibrated to fit 2007 U.S. data: Trends

I distribution of skills calibrated to match U.S. distribution of(adjusted gross) income from IRS public records

I trade cost parameters calibrated to match key U.S. trade moments




Building Blocks













Building Blocks













Building Blocks













Related Literature

I Trade models with heterogeneous workers: Itskhoki (2008) but also

I matching/sorting models (see Grossman, 2013, and Costinot andVogel, 2015, for recent surveys)

I models with imperfect labor markets (Helpman, Itskhoki, Redding...,and earlier Davidson and Matusz)

I Gains from trade and costly redistribution: Dixit and Norman(1986), Rodrik (1992), Spector (2001), Naito (2006)

I Old literature on Kaldor-Hicks: Kaldor (1939), Hicks (1939),Scitovszky (1941)

I Welfarist approach: Bergson (1938), Samuelson (1947), Diamond &Mirlees (1971), Atkinson (1970), Saez more recently

I Costly-redistribution: Kaplow (2008), Hendren (2014), Heathcoateet al. (2014)




Road Map

1. A Motivating Example

2. Economic Model

3. Calibration

4. Counterfactuals: Inequality and the Gains from Trade




Kaldor-Hicks PrincipleWelfarist CorrectionCostly Redistribution Correction

MOTIVATING EXAMPLE





A Motivating Example

I Consider a society composed of a measure one of individuals indexedby an ability ϕ and associated (real) earnings rϕ

I Agents’ preferences u defined over consumption cϕ, which equalsreal disposable income

rdϕ =[1− τ(rϕ)

]rϕ + Tϕ,

where τ (rϕ) is a nonlinear income tax and Tϕ a lump-sum transfer

I The cumulative distribution of ϕ in the population is Hϕ, while theassociated income distribution for real earnings is F (r)

I Society is evaluating the consequences of a trade liberalization thatwould shift F (r) from some initial Fr to F ′r .

I What are the welfare consequences of the move from Fr to F ′r ?








rdϕ =[1− τ(rϕ)

]rϕ + Tϕ,












rdϕ =[1− τ(rϕ)

]rϕ + Tϕ,












rdϕ =[1− τ(rϕ)

]rϕ + Tϕ,









The Kaldor-Hicks Principle: An Illustration

I Suppose only lump-sum transfers are used and government budget isbalanced so

∫TϕdHϕ = 0 and

∫rdϕdHϕ =

∫rdF (r)

I Compensating variation vϕ for individual of type ϕ:

u(rd′ϕ + vϕ

)= u

(rdϕ).

I After compensating losers, society has a surplus of:

−∫

vϕdHϕ =

∫rd′ϕ dHϕ −

∫rdϕdHϕ = R ′ − R

I Gains from trade = Aggregate Real Income Growth

W ′

W

∣∣∣∣Kaldor-Hicks

= 1 + µ ≡ R ′

R







∫TϕdHϕ = 0 and

∫rdϕdHϕ =

∫rdF (r)


u(rd′ϕ + vϕ

)= u

(rdϕ).


−∫

vϕdHϕ =

∫rd′ϕ dHϕ −



W ′

W


= 1 + µ ≡ R ′

R







∫TϕdHϕ = 0 and

∫rdϕdHϕ =

∫rdF (r)


u(rd′ϕ + vϕ

)= u

(rdϕ).


−∫

vϕdHϕ =

∫rd′ϕ dHϕ −



W ′

W


= 1 + µ ≡ R ′

R





Pros and Cons of the Kaldor-Hicks Principle

I Principle does not rely on interpersonal comparisons of utility

I u can be heterogeneous across agents

I relies on ordinal rather than cardinal preferences

I What if redistribution is not large enough to compensate the losers?

I agents might see a probability distribution over potential outcomes

I risk aversion ≈ inequality aversion (Vickery, 1945, Harsanyi, 1953)

I Even if some redistribution takes place, whenever it is costly,shouldn’t W ′/W reflect those costs?

I Example: Dixit and Norman (1986)































A Welfarist Correction

I Welfarist approach posits the existence of a social welfare function:

V =

∫u(rdϕ)dHϕ,

where u (·) is concave reflecting risk or inequality aversion

I Assume preferences feature constant inequality/risk aversion

u(rd)

=

(rd)1−ρ − 1

1− ρfor ρ ≥ 0

I With simple transformation, we have (c.f., Atkinson, 1970)

W =

[E((

rd)1−ρ

)]1/(1−ρ)

E (rd)× E

(rd)

= ∆× R

where ∆ ≤ 1 by Jensen’s inequality







V =

∫u(rdϕ)dHϕ,



u(rd)

=

(rd)1−ρ − 1

1− ρfor ρ ≥ 0


W =

[E((

rd)1−ρ

)]1/(1−ρ)

E (rd)× E

(rd)

= ∆× R








V =

∫u(rdϕ)dHϕ,



u(rd)

=

(rd)1−ρ − 1

1− ρfor ρ ≥ 0


W =

[E((

rd)1−ρ

)]1/(1−ρ)

E (rd)× E

(rd)

= ∆× R






Welfarist Correction: Two Special Cases

I Suppose Hϕ is such that the distribution of disposable income is

Pareto: ∆ =(

1+G1−G(1−2ρ)

)1/(1−ρ)1−G1+G

Lognormal: ∆ = exp{−ρ[Φ−1

(1+G

2

)]2}where G is the Gini coefficient of the distribution of rd

I W increases in mean income R but decreases in inequality G

I In both cases:

W ′

W

∣∣∣∣Welfarist

=∆ (G ′; ρ)

∆ (G ; ρ)× (1 + µ) ,

I This corresponds to consumption equivalent welfare changes





Welfarist Correction: Two Special Cases

I Suppose Hϕ is such that the distribution of disposable income is

Pareto: ∆ =(

1+G1−G(1−2ρ)

)1/(1−ρ)1−G1+G

Lognormal: ∆ = exp{−ρ[Φ−1

(1+G

2

)]2}where G is the Gini coefficient of the distribution of rd

I W increases in mean income R but decreases in inequality G

I In both cases:

W ′

W

∣∣∣∣Welfarist

=∆ (G ′; ρ)

∆ (G ; ρ)× (1 + µ) ,

I This corresponds to consumption equivalent welfare changes





A Costly Redistribution Correction

I Assume now that lump-sum transfers are not feasible andredistribution relies on an income tax-transfer system

I Focus on the particular case (as in Heathcoate et al., 2014) in which

1− τ (r) = k (r)−φ , (1)

for some constant k that ensures balanced budget

I Average net-of-tax rates decrease in reported income at a constantrate φ, which captures the degree of progressivity of the tax system

I Behavioral response to taxation: positive, constant elasticity ofreported income to the net-of-marginal-tax rate:

ε ≡ ∂r

∂ (1− τm (r))

1− τm (r)

r> 0








1− τ (r) = k (r)−φ , (1)




ε ≡ ∂r

∂ (1− τm (r))

1− τm (r)

r> 0








1− τ (r) = k (r)−φ , (1)




ε ≡ ∂r

∂ (1− τm (r))

1− τm (r)

r> 0





A Costly Redistribution CorrectionI Aggregate income can now be written as

R = (1− φ)ε(Er)1+ε

(Er1−φ)ε · E (r1+εφ)

× E (r) = Θ× R

I By Holder’s inequality, Θ ≤ 1; Θ is reduced by mean preservingmultiplicative spreads of the income distribution; Θ decreasing in φ

I Two parametric examples

Pareto: Θ = (1− φ)ε (1−φ)(1+G)−(1+εφ)2G(1−φ)(1+G)−2G

((1−φ)(1−G)

(1−φ)(1+G)−2G

)εLognormal: Θ = (1− φ)ε exp

{−φ

2ε(ε+1)

(1−φ)2

[Φ−1

(1+G

2

)]2}I More generally,

R ′

R=

Θ′

Θ× (1 + µR)






R = (1− φ)ε(Er)1+ε


× E (r) = Θ× R




((1−φ)(1−G)

(1−φ)(1+G)−2G


{−φ

2ε(ε+1)

(1−φ)2

[Φ−1

(1+G

2


R ′

R=

Θ′

Θ× (1 + µR)






R = (1− φ)ε(Er)1+ε


× E (r) = Θ× R




((1−φ)(1−G)

(1−φ)(1+G)−2G


{−φ

2ε(ε+1)

(1−φ)2

[Φ−1

(1+G

2

)]2}

I More generally,R ′

R=

Θ′

Θ× (1 + µR)






R = (1− φ)ε(Er)1+ε


× E (r) = Θ× R




((1−φ)(1−G)

(1−φ)(1+G)−2G


{−φ

2ε(ε+1)

(1−φ)2

[Φ−1

(1+G

2


R ′

R=

Θ′

Θ× (1 + µR)




Closed EconomyOpen EconomyTrade and Inequality

CONSTANT-ELASTICITY MODEL





A Constant-Elasticity ModelI Unit measure of heterogeneous workers with ability ϕ ∼ Hϕ

I Each worker provides its own differentiated good or task (CES)

I Linear production technology yϕ = ϕ`ϕ

I Real market revenue of worker ϕ is

rϕ = Q1−βyβββϕ ,

where Q is the quantity of final output in the economy

I Workers have utility over consumption and labor:

uϕ = cϕ −1

γ`γγγϕ, γ > 1

I Consumption equals after-tax income:

rϕ − T(rϕ)

= kr1−φφφϕ ,

and government runs balanced budget












uϕ = cϕ −1

γ`γγγϕ, γ > 1


rϕ − T(rϕ)

= kr1−φφφϕ ,













uϕ = cϕ −1

γ`γγγϕ, γ > 1


rϕ − T(rϕ)

= kr1−φφφϕ ,













uϕ = cϕ −1

γ`γγγϕ, γ > 1


rϕ − T(rϕ)

= kr1−φφφϕ ,






Equilibrium

I Distribution of disposable income (and utility) is shaped byunderlying distribution of ability and by parameters β, γ and φ:

cϕ ∝ ϕβ(1+ε)(1−φ)

1+εφ

where

εεε ≡ β

γ − βgoverns the elasticity of market income to marginal tax rates

I Higher after-tax income inequality when

I labor supply is more elastic (lower γ =⇒ higher ε)

I taxes are less progressive (lower φ)

I tasks are more substitutable (higher β)





Equilibrium

I Distribution of disposable income (and utility) is shaped byunderlying distribution of ability and by parameters β, γ and φ:

cϕ ∝ ϕβ(1+ε)(1−φ)

1+εφ

where

εεε ≡ β

γ − βgoverns the elasticity of market income to marginal tax rates

I Higher after-tax income inequality when

I labor supply is more elastic (lower γ =⇒ higher ε)

I taxes are less progressive (lower φ)

I tasks are more substitutable (higher β)





Social Welfare

I With a constant degree of inequality aversion ρρρ, we can write

W = ∆× Θ× W

where

∆ =

[E((

rd)1−ρ

)]1/(1−ρ)

E (rd)

Θ = (1 + εφ)(1 + εφ)(1 + εφ) (1− φ)εκκκ

[(Er)1+ε


]κκκand κ = 1/ (1− (1− β)(1 + ε)) > 1.

I ∆ is the same welfarist correction as in our example

I Θ is a slightly modified costly-redistribution correction

I W is welfare in a hypothetical ‘Kaldor-Hicks’ economy





A First Look at the Data

I Let us first use our closed-economy model to interpret these trends

1980 1985 1990 1995 2000 20050.8

0.9

1

1.1

1.2

1.3

1.4

1.5Real Adjusted Gross Income in the United States (1979-2007)

Mean IncomeMedian Income10th Percentile





Calibration: U.S. Income Growth (1979-2007)

I Use U.S. Individual Income Tax Public Use Sample to calibratedistribution of market income

I approximately 150,000 anonymized tax returns per year

I use NBER weights to ensure this is a representative sample

I we map market income to adjusted gross income (AGI) in line 37 ofIRS Form 1040

I Use CBO data on before-tax and after-tax/transfer income tocalibrate the degree of tax progressivity φ

I Elasticity of taxable income is ε = 0.5 (Chetty, 2012)

I Elasticity of substitution = 5 (β = 4/5)I slightly higher than in BEJK (2003) and Broda and Weinstein (2006)

I Experiment with various values of ρ (benchmark ρ = 1)

























































Calibrating the Income Distribution

I Lognormal provides a reasonably good approximation, but it does apoor fit for the right-tail of the distribution, which looks Pareto

5 7 9 11 13

log(r)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Income Distribution CDF

Data (Non-Parametric Fit)Lognormal Fit

0 1 2 3 4 5

r×10

5

1

1.5

2

2.5

Empirical Pareto Coefficient





Calibrating Tax Progressivity

8 10 12 14

Log Pre-Tax rϕ

8

9

10

11

12

13

14

15

LogPost-Taxrϕ

1980

1− φ =0.759

R2 =0.983

8 10 12 14

Log Pre-Tax rϕ

8

9

10

11

12

13

14

15

LogPost-Taxrϕ

1985

1− φ =0.816

R2 =0.986

8 10 12 14

Log Pre-Tax rϕ

8

9

10

11

12

13

14

15

LogPost-Taxrϕ

1990

1− φ =0.813

R2 =0.987

8 10 12 14

Log Pre-Tax rϕ

8

9

10

11

12

13

14

15

LogPost-Taxrϕ

1995

1− φ =0.795

R2 =0.992

8 10 12 14

Log Pre-Tax rϕ

8

9

10

11

12

13

14

15

LogPost-Taxrϕ

2000

1− φ =0.84

R2 =0.994

8 10 12 14

Log Pre-Tax rϕ

8

9

10

11

12

13

14

15

LogPost-Taxrϕ

2005

1− φ =0.839

R2 =0.995





U.S. Progressivity Over Time

1979 1983 1987 1991 1995 1999 2003 2007

Year

0.1

0.15

0.2

0.25

0.3φ





Social Welfare and Counterfactuals

Path of Corrections





Social Welfare and Counterfactuals

Path of Corrections





OPEN ECONOMY MODEL





Open Economy: Environment

I Consider a world economy with N + 1 symmetric countries

I Agents can market their output locally or in any other of N countries

I Trade/Offshoring involves two types of additional costs

1. Symmetric iceberg cost τττ (reduces revenue per unit shipped)

2. Fixed cost f (n) of exporting to n-th foreign market: f (n) = fxfxfxnααα

I α 6= 0 helps smooth effect of trade integration on income distribution

I Sale revenue is now

rϕ = Υ1−βnϕ Q1−βyβϕ , (2)

whereΥnϕ = 1 + nϕτ

− β1−β

and yϕ = ϕ`ϕ is total output















− β1−β
















− β1−β
















− β1−β






Open Economy: TaxationI Government only observes market revenue of individuals and taxes

according to the same tax schedule T (r) in (1)I exporting costs f (nϕ) are not deductible from taxes

I Disposable income and consumption are thus

cϕ = kr1−φϕ − fx

nϕ∑n=1

nα, (3)

I Agents choose labor input `ϕ and market access investment nϕ tomaximize utility given the revenue function (2) and budgetconstraint (14)

I Given symmetry, goods market clearing imposes

Q =

(∫ 1

0

Υ1−βnϕ yβϕdHϕ

)1/β









nϕ∑n=1

nα, (3)



Q =

(∫ 1

0


)1/β









nϕ∑n=1

nα, (3)



Q =

(∫ 1

0


)1/β





Trade and InequalityI Result: Relative to autarky, trade increases inequality of revenues

and utilities

rϕQ∝

ϕβ(1+ε)(1−φ)

1+εφ , ϕ < ϕx1 ,

Υ(1−β)(1+ε)(1−φ)

1+εφ

1 ϕβ(1+ε)(1−φ)

1+εφ , ϕ < ϕx2,

......

Υ(1−β)(1+ε)(1−φ)

1+εφ

N ϕβ(1+ε)(1−φ)

1+εφ ϕ ≥ ϕxN

Υn = 1+nτ−β

1−β

I Two limiting cases:

I no agent exports (ϕx1 →∞)I all agents export (ϕxN → ϕmin)

rϕQ

=rϕ,aut

Qaut∝ ϕ

β(1+ε)(1−φ)1+εφ





Trade and Inequality (cont.)I Relative to autarky, trade increases relative sale revenue of

high-ability workers but reduces that of low-ability workers

Productivity0 100 200 300 400 500 600 700 800 900 1000

Rel

ativ

e R

even

ues,

r/R

0

1

2

3

4

5

6

AutarkyOpen Economy





Trade and Inequality (cont.)

I Although inequality could eventually decline with trade, we are farfrom that region

1 1.5 2 2.5 3 3.5 4

Variable Trade Cost τ

1

1.01

1.02

1.03

1.04

1.05

Gini Ratio

τ2007

τ1979

1 1.5 2 2.5 3 3.5 4

Variable Trade Cost τ

1

1.02

1.04

1.06

1.08

1.1

Variance(r/Mean(r)) Ratio

τ2007

τ1979

rϕ - Pre-Taxkr1−φ

ϕ - Post-Tax




CalibrationCalibrated Welfarist CorrectionCalibrated Costly Redistribution Correction

Calibration and Counterfactuals: Road Map

I We first calibrate the model to 2007 U.S. dataI as in the closed economy but with additional trade moments

I We then explore the implication of a move to autarky on

1. Aggregate Income

2. Income Inequality

I We use the model to gauge the quantitative importance of the twocorrections developed above

W =

[E(uϕ)1−ρ

] 11−ρ

Euϕ× Euϕ

W× W = ∆T ×ΘT × WT .

1. How large is W ′/W for different degrees of inequality aversion?

2. How large would W ′/W be in the absence of costly redistribution?








1. Aggregate Income



W =

[E(uϕ)1−ρ

] 11−ρ

Euϕ× Euϕ

W× W = ∆T ×ΘT × WT .










1. Aggregate Income



W =

[E(uϕ)1−ρ

] 11−ρ

Euϕ× Euϕ

W× W = ∆T ×ΘT × WT .










1. Aggregate Income



W =

[E(uϕ)1−ρ

] 11−ρ

Euϕ× Euϕ

W× W = ∆T ×ΘT × WT .







Calibration

I For our benchmark results, hold the following primitives constant

1. As in closed economy, set β = 4/5 and γ = 2.4, so that ε = 0.5

2. Number of countries N = 5 (i.e. U.S. is 18.3% of world GDP)

I Jointly calibrate trade parameters (τ , fx , α) and the abilitydistribution Hϕ to match:

1. 2007 trade share of 7.7% from NIPA =⇒ τ = 2.15

2. Share of exporter sales in total sales = 61.8% =⇒ fx =$675

3. Skewness of exporting firms’ sales so that firms that export to n > 1destinations account for 88.9% of total exporters’ sales =⇒ α = 0.55

4. The 2007 distribution of market income from the IRS data Implied Hϕ

I In the counterfactuals, we then set τ1979 = 2.30 to match 1979 tradeshare of 4.9% (holding all else equal); also τautarky = +∞





Calibration














Calibration














Calibration: Progressivity

I Note from (1) that ln rd = ln k + (1− φ) ln r (ϕ) =⇒ φ = 0.147

9 10 11 12 13 14 15

Log Pre-Tax rϕ

9

10

11

12

13

14

15LogPost-Taxrϕ

2007

y = 0.853x+1.661

R2 =0.995





Calibrated Welfare Gains from Trade and Inequality

I Calibrated welfare gains from trade are higher, the higher is thelabor supply elasticity ε (Arkolakis and Esposito, 2014)

I But relative to autarky trade induces more inequality when ε is high

% Consumption Gains % Welfare Gains (ρ = 0) % Increase in Giniτ1979 τ = ∞ τ1979 τ = ∞ τ1979 τ = ∞

ε = 0.25 0.8 2.4 0.8 2.3 0.4 1.1ε = 0.5 1.2 3.4 1.1 3.2 0.5 1.3ε = 1 2.0 6.0 1.9 5.6 0.6 1.6





Welfarist Correction

I Welfarist correction is higher, the higher is ρ and the lower is ε

I With log utility (ρ = 1) and a labor supply elasticity of ε = 0.5,welfare gains are 23% lower

0 0.5 1 1.5 2

Degree of Risk/Inequality Aversion ρ

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Welfarist Modified Statistic

ε = 0.5

τ1979

τ = ∞

0 0.5 1 1.5 2

Degree of Risk/Inequality Aversion ρ

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Welfarist Modified Statistic

ε = 0.25

ε = 1





Costly Redistribution CorrectionI Costly redistribution correction is higher, the higher is ε

I When ε = 0.5, welfare gains would be 10% higher (for τ1979) and16% highe (for τautarky ) with costless redistribution

0 0.2 0.4 0.6 0.8 1

Elasticity of Taxable Income ε

0.75

0.8

0.85

0.9

0.95

1

Costly Redistribution Modified Statistic

ε = 0.5ε = 0.5ε = 0.5ε = 0.5ε = 0.5

τ1979

τ = ∞





Robustness and Additional Exercises

0.65 0.7 0.75 0.8 0.85 0.9

β

0.5

0.6

0.7

0.8

0.9

1

Modified Statistics

∆stat, τ1979∆stat, τ = ∞

Θstat, τ1979Θstat, τ = ∞

40 50 60 70 80

M2 %

0.5

0.6

0.7

0.8

0.9

1

Modified Statistics

75 80 85 90 95

M3 %

0.5

0.6

0.7

0.8

0.9

1

Modified Statistics

More Robustness





Conclusions

I Trade-induced inequality is partly mitigated via a progressive incometax system

I Still, compensation is not full so trade induces an increase in thedistribution of disposable income

I Is the Kaldor-Hicks principle really free of value judgements?

I Income taxation induces behavioral responses that affect theaggregate income response to trade integration

I Shouldn’t the Kaldor-Hicks principle adjust for these inefficiencies?

I In this paper, we have developed welfarist and costly redistributioncorrections to standard measures of the gains from trade integration

I Under plausible parameter values, these corrections are nonneglible





Conclusions












Conclusions












Conclusions












Conclusions












Conclusions

“If, as will often happen, the best methods of compensation feasibleinvolve some loss in productive efficiency, this loss will have to be takeninto account.”

Hicks (1939, p. 712)


Appendix

Trade Integration and Income Inequality in the U.S.

1979 1983 1987 1991 1995 1999 2003 2007

4.0%

5.0%

6.0%

7.0%

8.0%

0.47

0.49

0.51

0.53

0.55

0.57

0.59

0.61

Trade/Gross OutputGini of Market Income

BACK


Appendix

Evolution of ∆ and Θ Over Time

0.55 0.6 0.65 0.7 0.75 0.8": Inequality Aversion

0.89

0.9

0.91

0.92

0.93

0.94

(1+0?

)#5: C

ostly

Red

istri

butio

n

(",(1+0? )# 5 ) Phase Diagram, ;=1

BACK


Appendix

Implied 2007 Ability Distribution Hϕ

-4 -2 0 2 4 6 8 10 12 14ln(')

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45NonparametricLognormal Approximation

BACK


Appendix

Robustness and Additional Exercises

Benchmark Avg. φ Endog. φ N = 3 N = 7 Manuf. LN ϕ(a) (b) (c) (d) (e) (f) (g)

∆Stat 1979 0.77 0.81 0.44 0.77 0.77 0.77 0.76Autarky 0.77 0.82 0.71 0.77 0.78 0.77 0.78

ΘStat 1979 0.91 0.88 1.81 0.93 0.90 0.99 0.93Autarky 0.86 0.81 1.04 0.88 0.85 0.94 0.83

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Globalization, Inequality and Welfare · 2016. 9. 7. · Globalization, Inequality and Welfare Pol Antr as Harvard University Alonso de Gortari Harvard University Oleg Itskhoki Princeton